Improving Multiple-Model Context-Aided Tracking through an Autocorrelation Approach

Proceedings of: 15th International Conference on Information Fusion (FUSION), Singapore, 9-12 July 2012This paper continues a previous work, where the context-aided tracker "ConTracker" was used to detect suspicious behaviors in maritime vehicle trajectories. ConTracker takes into account map-based contextual information - which includes water depth, shipping channels and areas/buildings with a high strategy value - to determine anomalies in ship trajectories. The different areas act as repellers or attractors that modify the expected trajectory of the tracked vessel. In the original scheme, a multiple-model adaptive estimator (MMAE) is used to estimate the noise parameters of the tracking system: sudden increases on the output reflect unexpected maneuvers - such as entering a forbidden area - that are translated as alarms. The work presented here shows the results obtained by implementing a generalized version of the multiple-model adaptive estimator (GMMAE). While the former approach uses information of the last cycle to update the weight/importance of each model, our proposal calculates a likelihood value based on the time-domain autocorrelation function of the last few indicators. GMMAE provides a much faster response, which ultimately leads to a general performance boost: alarms are faster and clearer. Compared with previous works, GMMAE is particularly effective returning back to normal state after an alarm has been raised: this results in alarms with a better defined duration. Results are presented over several simulated trajectories, featuring a variety of realistic anomalies which are correctly identified. They include direct comparison with the previous approach, for an objective demonstration of the achieved improvement.This work was supported in part by Projects CICYT TIN2011-28620-C02-01, CICYT TEC2011-28626-C02- 02, CAM CONTEXTS (S2009/TIC-1485) and DPS2008- 07029-C02-02.Publicad

The Space Object Ontology

Achieving space domain awareness requires the identification, characterization, and tracking of space objects. Storing and leveraging associated space object data for purposes such as hostile threat assessment, object identification, and collision prediction and avoidance present further challenges. Space objects are characterized according to a variety of parameters including their identifiers, design specifications, components, subsystems, capabilities, vulnerabilities, origins, missions, orbital elements, patterns of life, processes, operational statuses, and associated persons, organizations, or nations. The Space Object Ontology provides a consensus-based realist framework for formulating such characterizations in a computable fashion. Space object data are aligned with classes and relations in the Space Object Ontology and stored in a dynamically updated Resource Description Framework triple store, which can be queried to support space domain awareness and the needs of spacecraft operators. This paper presents the core of the Space Object Ontology, discusses its advantages over other approaches to space object classification, and demonstrates its ability to combine diverse sets of data from multiple sources within an expandable framework. Finally, we show how the ontology provides benefits for enhancing and maintaining longterm space domain awareness

Attitude Estimation Using Modified Rodrigues Parameters

In this paper, a Kalman filter formulation for attitude estimation is derived using the Modified Rodrigues Parameters. The extended Kalman filter uses a gyro-based model for attitude propagation. Two solutions are developed for the sensitivity matrix in the Kalman filter. One is based upon an additive error approach, and the other is based upon a multiplicative error approach. It is shown that the two solutions are in fact equivalent. The Kalman filter is then used to estimate the attitude of a simulated spacecraft. Results indicate that then new algorithm produces accurate attitude estimates by determining actual gyro biases

An MME-based attitude estimator using vector observations

In this paper, an optimal batch estimator and filter based on the Minimum Model Error (MME) approach is developed for three-axis stabilized spacecraft. Three different MME algorithms are developed. The first algorithm estimates the attitude of a spacecraft using rate measurements. The second algorithm estimates the attitude without using rate measurements. The absence of rate data may be a result of intentional design or from unexpected failure of existing gyros. The third algorithm determines input-torque modeling error trajectories. All of the algorithms developed in this paper use attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc.). Results using these new algorithms indicate that an MME-based approach accurately estimates the attitude, rate, and input torque trajectories of an actual spacecraft

Attitude Estimation for Large Field-of-View Sensors

The QUEST measurement noise model for unit vector observations has been widely used in spacecraft attitude estimation for more than twenty years. It was derived under the approximation that the noise lies in the tangent plane of the respective unit vector and is axially symmetrically distributed about the vector. For large field-of-view sensors, however, this approximation may be poor, especially when the measurement falls near the edge of the field of view. In this paper a new measurement noise model is derived based on a realistic noise distribution in the focal-plane of a large field-of-view sensor, which shows significant differences from the QUEST model for unit vector observations far away from the sensor boresight. An extended Kalman filter for attitude estimation is then designed with the new measurement noise model. Simulation results show that with the new measurement model the extended Kalman filter achieves better estimation performance using large field-of-view sensor observations

Deterministic Relative Attitude Determination of Three-Vehicle Formations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77266/1/AIAA-42849-367.pd

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown

Research Opportunities in Contextualized Fusion Systems. The Harbor Surveillance Case

Proceedings of: International Workshop of Intelligent Systems for Context-Based Information Fusion (ISCIF 2011) associated to 11th International Work-Conference on Artificial Neural Networks, IWANN, Torremolinos-Málaga, Spain, June 8-10, 2011.The design of modern Information Fusion (IF) systems involves a complex process to achieve the requirements in the selected applications, especially in domains with a high degree of customization. In general, an advanced fusion system is required to show robust, context-sensitive behavior and efficient performance in real time. It is necessary to exploit all potentially relevant sensor and contextual information in the most appropriate way. Among modern applications for IF technology is the case of surveillance of complex harbor environments that are comprised of large numbers of surface vessels, high-value and dangerous facilities, and many people. The particular conditions and open needs in the harbor scenario are reviewed in this paper, highlighting research opportunities to explore in the development of fusion systems in this area.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC and CAM CONTEXTS S2009/TIC-1485.Publicad

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented